Pulse shaping is the technique which controls the ultra-short pulse shape, and it became
of great technological interest because of its potential applications in laser pulse
compression, digital communications, microscopy etc. We demonstrate the idea of
pulse-shaping technique and pulse propagation with low energy losses in a resonant
linear absorbing medium. This thesis presents the results of a study of the propagation
of Gaussian and hyperbolic secant ultrashort chirped and chirp-free pulses in
homogeneously and inhomogeneously broadened resonant linear absorbers. Changes
to the pulse shape and energy loss factor are presented as the pulse propagates in
the absorber. The Fast Fourier method is used to numerically determine both the
normalized intensity profile and the pulse spectrum.
Our results show that, for pulse durations shorter than the relaxation time, chirped
pulses in absorbing media obey the area theorem, with their shape changing with the
propagation distance. Simulation results of the spectra of chirped pulses clearly show
the burning of a spectral ’hole’ as the pulse propagates, with the pulse energy pushed
away towards the wings. When compared to chirp-free pulses, chirped pulses reshape
faster and develop wings in their tail due to initial phase modulation.
Simulation results of the energy loss factor show that chirped pulses propagating
in resonant linear absorbers sustain less energy losses than do chirp-free pulses. A
comparison of chirped secant and Gaussian pulses shows that secant pulses propagate
with lower energy losses.
Analytic solutions are presented for long-distance asymptotic expressions of initial
rms spectral bandwidth as well as for the attenuation factor of chirped Gaussian
pulses. These analytical results are in agreement with numerical simulations. The
comparison of energy losses of short chirped Gaussian pulses and long pulses of any
profile in linear absorbers is also discussed in the thesis.